# Thread: Finding solutions for trig equations

1. ## Finding solutions for trig equations

Im sure this is a trivial problem for many, but not having done this for a while im a bit rusty and cant figure it out

I have the answers to the following question, but i do not know how to calculate them from the first:

Find all the solutions to the following equation

Sin( ((5x)/2) + 15°) = 0.34

Where 0°≤x≥360°

My attempt

sin-1(0.34)=19.88

19.88-15 = 4.88

(4.88*2)/5 = 1.95

How are the other answer worked out from here?

Any input appreciated

Thanks

2. ## Re: Finding solutions for trig equations

Remember that there are two quadrants where sin(x) = 0.34 (both first and second quadrant), so x may be either 19.88 degrees or 180 -19.88 = 160.12 degrees. And furher since the final answer must be in the range 0 < x < 360, that means that 5x/2+15 will be in the range 15 to 915 degrees. Which means in addition to 5x/2= 19.88 you also have 5x/2=19.88 + 360 and 5x/2+15 = 19.88+ 2x360 degrees. Same with 5x/2+15=160.12, 5x/2+15= 160.12+360, etc.

One other comment - no fault of yours given the answers in the form that that you were given, but it drives me crazy to see answers taken out to 10 decimal places of accuracy when the data you were given is only two decimal places. The proper answer for the first one is x=1.95, not x= 1.950749628.

3. ## Re: Finding solutions for trig equations

Thanks, that sorted the problem. Do you know how i would rearrange cos(56deg -3x) = -0.305. iv tried to work this out as inverse of cos 107.758 then use (107.758-56)/-3 which gives me the wrong answers, i also tried to get the other cos angle as 107.758-90 = 17.758 then staying in the negative quadrant of cos 270 + 17.758 = 287.758 to which iv got the wrong answers

Thanks

4. ## Re: Finding solutions for trig equations

Originally Posted by MMCS
Do you know how i would rearrange cos(56deg -3x) = -0.305. iv tried to work this out as inverse of cos 107.758 then use (107.758-56)/-3 which gives me the wrong answers,
I think it gives the correct answer of x = -17.25 degrees. What have you been told is the answer?

Originally Posted by MMCS
i also tried to get the other cos angle as 107.758-90 = 17.758
Remember for that cos(x) = cos(-x) = 360 - cos(x). So try -107.8 degrees, which is the same as +252.2 degrees.

5. ## Re: Finding solutions for trig equations

Inspect roots before finding their numerical values (Radian):